Geodesic
The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in~$L_1$ equal to zero on a~given set
Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 1-35.

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The precise structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere (a.e.) of Fourier series of functions in the class $L_1(T^N)$, $N\geqslant1$, $T^N[0,2\pi]^N$, and vanishing on a given measurable set $E$ is found (in the case $N\geqslant2$ this is done for both rectangular and square summation). Bibliography: 21 titles. 
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I. L. Bloshanskii. The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in~$L_1$ equal to zero on a~given set. Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 1-35. http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a0/

[1] Carleson L., “On convergence and growth of partial sums of Fourier series”, Acta Math., 116 (1966), 135–157 | DOI | MR | Zbl

[2] Hunt R., “On the convergence of Fourier series, ortogonal Expansions and their Continuous Analogues”, Proc. Conf. (Edwardsville Ill. 1967), Southern Illinouis Univ. Press (Carbondale Ill.), 1968, 235–255 | MR | Zbl

[3] Kolmogoroff A., “Une serie de Fourier de Fourier–Lebesque divergente presque partout”, Fund Math., 4 (1923), 324–328 | Zbl

[4] Bari N. K., Trigonometricheskie ryady, Fizmatlit, M., 1961 | MR

[5] Menshov D. E., “O ryadakh Fure ot summiruemykh funktsii”, Tr. Mosk. matem. ob-va, 1, 1951, 5–38

[6] Bloshanskii I. L., “O raskhodimosti ryada Fure pochti vsyudu na zadannom mnozhestve i skhodimosti k nulyu vne ego”, Dokl. AN SSSR, 280:4 (1985), 777–780 | MR

[7] Bloshanskii I. L., “Dva kriteriya slaboi obobschennoi lokalizatsii dlya kratnykh trigonometricheskikh ryadov Fure funktsii iz $L_p$, $p\geqslant1$”, Izv. AN SSSR. Ser. matem., 49:2 (1985), 243–282 | MR

[8] Tevzadze N. R., “O skhodimosti dvoinogo ryada Fure funktsii, summiruemoi s kvadratom”, Soobsch. AN GruzSSR, 58:2 (1970), 277–279 | MR | Zbl

[9] Sjolin P., “Convergence almost everywhere of certain singular integrals and multiple Fourier series”, Arkiw Math., 9:1 (1971), 65–90 | DOI | MR

[10] Bloshanskii I. L., “Generalized localization and convergence tests for double trigonometric Fourier series of functions from $L_p$, $p>1$”, Analysis Math., 7:1 (1981), 3–36 | DOI | MR

[11] Bloshanskii I. L., “Obobschennaya lokalizatsiya pochti vsyudu i skhodimost dvoinykh ryadov Fure”, Dokl. AN SSSR, 242:1 (1978), 11–13 | MR

[12] Bloshanskii I. L., “O geometrii izmerimykh mnozhestv v $N$-mernom prostranstve, na kotorykh spravedliva obobschennaya lokalizatsiya dlya kratnykh trigonometricheskikh ryadov Fure funktsii iz $L_p$, $p>1$”, Matem. sb., 121(163) (1983), 87–110 | MR

[13] Bloshanskii I. L., “Obobschennaya lokalizatsiya dlya kratnykh ryadov Fure i geometriya izmerimykh mnozhestv v $N$-mernom prostranstve”, Dokl. AN SSSR, 266:4 (1982), 780–783 | MR

[14] Bloshanskii I. L., “O kriteriyakh slaboi obobschennoi lokalizatsii v $N$-mernom prostranstve”, Dokl. AN SSSR, 271:6 (1983), 1294–1298 | MR

[15] Tonelli L., Serie trigonometriche, Bologna, 1928

[16] Zigmund A., Trigonometricheskie ryady, t. 2, Mir, M., 1965 | MR

[17] Hardy G. H., Wright E. M., An introduction to the theory of numbers, Oxford, 1938 | MR

[18] Körner T. W., “Everywhere divergent Fourier series”, Colloq. Math., 45:1 (1981), 103–118 | MR | Zbl

[19] Stein E. M., “On limits of sequences of operators”, Ann. Math., 74:1 (1961), 140–170 | DOI | MR | Zbl

[20] Kakhan Zh.-P., Sluchainye funktsionalnye ryady, Mir, M., 1973 | MR | Zbl

[21] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl